Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1469–1497 | Cite as

Event-Triggered Sampled-Data Consensus of Nonlinear Multi-Agent Systems with Control Input Losses

  • Mali XingEmail author
  • Feiqi Deng


This paper investigates the leader-following consensus problem for multi-agent systems with event-triggered mechanism and control packet losses. Based on the local synchronization error, event-triggered mechanisms are proposed in order to reduce the number of controller update. The control packet may lose due to unreliability of communication channel. With the assumption that once the packet loss happens the controller will be set to zero, sufficient consensus criteria for multi-agent system with event-triggered mechanism and control packet losses is obtained. It is also shown that the interplay among the allowable packet loss rate, event-triggered mechanism and sampling period. An illustrative example is given to demonstrate the effectiveness of the theoretical results.


Consensus control packet losses event-triggered mechanism multi-agent systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Olfati-Saber R and Murray R M, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automatic Control, 2004, 49(9): 1520–1533.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Jadbabaie A, Lin J, and Morse A S, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automatic Control, 2003, 48(6): 988–1001.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Okubo A, Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds, Advances in Biophysics, 1986, 22: 1–94.CrossRefGoogle Scholar
  4. [4]
    Yang P, Freeman R A, and Lynch K M, Multi-agent coordination by decentralized estimation and control, IEEE Trans. Automatic Control, 2008, 53(11): 2480–2496.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Fridman E, Seuret A, and Richard J P, Robust sampled-data stabilization of linear systems: an input delay approach, Automatica, 2004, 40(8): 1441–1446.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Zhang W A and Yu L, Stabilization of sampled-data control systems with control inputs missing, IEEE Trans. Automatic Control, 2010, 55(2): 447–452.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Wu Z G, Shi P, Su H, et al., Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay, IEEE Trans. Neural Networks and Learning Systems, 2013, 24(8): 1177–1187.CrossRefGoogle Scholar
  8. [8]
    Rakkiyappan R, Dharani S, and Cao J, Synchronization of neural networks with control packet loss and time-varying delay via stochastic sampled-data controller, IEEE Trans. Neural Networks and Learning Systems, 2015, 26(12): 3215–3226.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Rakkiyappan R, Sakthivel N, and Cao J, Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays, Neural Networks, 2015, 66: 46–63.CrossRefzbMATHGoogle Scholar
  10. [10]
    Hu Z and Deng F, Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling, Int. J. of Robust and Nonlinear Control, 2017, 27(1).Google Scholar
  11. [11]
    Peng C, Han Q L, and Yue D, To transmit or not to transmit: A discrete event-triggered communication scheme for networked takagi-sugeno fuzzy systems, IEEE Trans. Fuzzy Systems, 2013, 21(1): 164–170.CrossRefGoogle Scholar
  12. [12]
    Garcia E, Cao Y, and Casbeer D W, Decentralized event-triggered consensus with general linear dynamics, Automatica, 2014, 50(10): 2633–2640.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Zhang H, Feng G, Yan H, et al., Observer-based output feedback event-triggered control for consensus of multi-agent systems, IEEE Trans. Industrial Electronics, 2014, 61(9): 4885–4894.CrossRefGoogle Scholar
  14. [14]
    Liu W, Yang C, Sun Y, et al., Observer-based event-triggered tracking control of leader-follower systems with time delay, Journal of Systems Science and Complexity, 2016, 29(4): 865–880.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Hu W, Liu L, and Feng G, Consensus of linear multi-agent systems by distributed event-triggered strategy, IEEE Trans. Cybernetics, 2016, 46(1): 148–157.CrossRefGoogle Scholar
  16. [16]
    Dimarogonas D V, Frazzoli E, and Johansson K H, Distributed event-triggered control for multiagent systems, IEEE Trans. Automatic Control, 2012, 57(5): 1291–1297.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Li H, Liao X, Huang T, et al., Event-triggering sampling based leader-following consensus in second-order multi-agent systems, IEEE Trans. Automatic Control, 2015, 60(7): 1998–2003.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Qu F L, Guan Z H, He D X, et al., Event-triggered control for networked control systems with quantization and packet losses, Journal of the Franklin Institute, 2015, 352(3): 974–986.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Zhang T and Li J M, Asynchronous event-triggered control of multi-agent systems with Sigma- Delta quantizer and packet losses, Journal of the Franklin Institute, 2016, 353(8): 1781–1808.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Garcia E, Cao Y C, and Casbeer D W, Decentralised event-triggered consensus of double integrator multi-agent systems with packet losses and communication delays, Iet Control Theory & Applications, 2016, 10(15): 1835–1843.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Yan C, Yu M, Xie G M, et al., Event-triggered control for multiagent systems with the problem of packet losses and communication delays when using the second-order neighbors’ information, Abstract and Applied Analysis, 2014, 2014: 1–7.Google Scholar
  22. [22]
    Yu M, Yan C, Xie D M, et al., Event-triggered tracking consensus with packet losses and timevarying delays, IEEE/CAA Journal of Automatica Sinica, 2016, 3(2): 165–173.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Zhang Q, Lu J, Lu J, et al., Adaptive feedback synchronization of a general complex dynamical network with delayed nodes, IEEE Trans. Circuits and Systems II: Express Briefs, 2008, 55(2): 183–187.CrossRefGoogle Scholar
  24. [24]
    Wang Z, Liu Y, Li M, et al., Stability analysis for stochastic cohen-grossberg neural networks with mixed time delays, IEEE Trans. on Neural Networks, 2006, 17(3): 814–820.CrossRefGoogle Scholar
  25. [25]
    Wang Z, Wang Y, and Liu Y, Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays, IEEE Trans. Neural Networks, 2010, 21(1): 11–25.CrossRefGoogle Scholar
  26. [26]
    Liu Y, Wang Z, Liang J, et al., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Trans. Systems, Man, and Cybernetics, Part B (Cybernetics), 2008, 38(5): 1314–1325.CrossRefGoogle Scholar
  27. [27]
    Hespanha J P and Morse A S, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control, 1999, 3: 2655–2660.Google Scholar
  28. [28]
    Zhang W B, Tang Y, Huang T W, et al., Sampled-data consensus of linear multi-agent systems with packet losses, IEEE Trans. on Neural Networks and Learning Systems, 2016, 28(11): 2516–2527.MathSciNetCrossRefGoogle Scholar
  29. [29]
    Chen T, Liu X, and Lu W, Pinning complex networks by a single controller, IEEE Trans. Circuits and Systems I: Regular Papers, 2007, 54(6): 1317–1326.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Heemels W, Donkers M, and Teel A R, Periodic event-triggered control for linear systems, IEEE Trans. Automatic Control, 2013, 58(4): 847–861.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    Yue D, Tian E, and Han Q L, A delay system method for designing event-triggered controllers of networked control systems, IEEE Trans. Automatic Control, 2013, 58(2): 475–481.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Park P G, Ko J W, and Jeong C, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 2011, 47(1): 235–238.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Seuret A and Gouaisbaut F, Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 2013, 49(9): 2860–2866.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    Lee T H and Ju H P, Stability analysis of sampled-data systems via free-matrix-based timedependent discontinuous Lyapunov approach, IEEE Trans. on Automatic Control, 2017, 62(7): 3653–3657.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina

Personalised recommendations